A168314 - OEIS

%I #11 Aug 28 2024 09:36:40

%S 1,1,3,5,13,29,71,165,401,957,2315,5561,13437,32377,78191,188617,

%T 455425,1099137,2653699,6405733,15465165,37334149,90133463,217596445,

%U 525326353,1268238029,3061802411,7391815977,17845434365,43082619953,104010674271,251103812113

%N Eigensequence of triangle A168313.

%C Conjectured convergent of a(n)/a(n-1) = (1+sqrt(2)). E.g.: a(19)/a(18) = 2653699/1099137 = 2.4143478...

%F Equals the eigensequence of triangle A168313 = lim_{n->oo} M^n where M = A168313 shifted down one row and inserting a "1" at top.

%F Equals the left column vector as a sequence.

%o (Python)

%o a = [1]

%o for n in range(30):

%o     a.append(2*sum(a[n//2:-1]) + a[-1])

%o print(a) # _Andrey Zabolotskiy_, Aug 28 2024

%Y Cf. A168313, A168315.

%K eigen,nonn

%O 1,3

%A _Gary W. Adamson_, Nov 22 2009

%E Terms a(20) and beyond from _Andrey Zabolotskiy_, Aug 28 2024